44 REPORT — 1873. 



and several other works that we have examined will be noticed at length in a 

 future Keport. 



On Eheticns's other works see Pitiscus, 1613, below. 

 Gcrnerth has given a list of 598 errors that he found in the first seven or 

 eight figures of the ten-decimal canon in the ' Zeitschrift f. d. osterr. Gymn.' 

 YI. Heft, S. 407 (also published separately). He also gives an account of the 

 contents of the ' Opus Palatinum,' from which it appears tliat in his copy the 

 difterent parts of it were bound up in a diflPerent order from that in which they 

 appear in the copy wc have examined (which seems to be anomalous in this 

 respect) ; and he omits the 121 pp. of the ' Meteoroscopium.' The great in- 

 accuracy of the small canon is also noticed by him ; and it is on this account 

 that he gives uo errata list for it. 



Pitiscus, 1613 [T. I.] (pp. 2-271, calculated by Rheticus). Natural 

 sines for every ten seconds throughout the quadrant, to 15 places, semiqua- 

 drantally arranged, with first, second, and third differences. (On p. 13, Fer- 

 pendkulum and Basis are printed instead of Sinus and Sinus complementi). 



[T. II.] (pp. 2-61, calculated by Rheticus). Natural sines for every 

 second from 0° to 1°, and from 89° to 90°, to 15 places, with first and second 

 diff'erences. 



[T. III. and IV.] (pp. 3-15). The lengths of the chords of a few angles, 

 to 25 places, with verifications &e., followed by natural sines and cosines 

 for the tenth, twentieth, and fiftieth second in every minute to 35', to 22 

 places, with first, second, third, fourth, and sometimes fifth differences. 



The numbering of the pages thus recommences in each table (except. T. 

 IV.) ; and each has a separate titlepage. On the first two the date is printed 

 do . lo . XIII. instead of cIo . loc . xiii. 



The rescue of the MS. of this work from destruction by Pitiscus (as told by 

 himself in the preface) forms a striking episode in the history of mathematical 

 tables. The alterations and emendations in the earlier part of the corrected 

 edition of the ' Opus Palatinum ' were made by Pitiscus; and he remarked that 

 a table of sines to more places than ten was requisite to enable the corrections 

 to be conveniently made. He had his suspicions that Rheticus had himself cal- 

 culated a ten-second canon of sines to fifteen decimal places; and on application 

 to Valentine Otho, the original editor of the ' Opus Palatinum,' the latter, who 

 was then an old man, acknowledged that such was the case, but could not 

 remember where the MS. was (" ob memoriaj senilis debilitatem "). He thought 

 that perhaps he had left it at Wittemberg ; and accordingly Pitiscus sent a 

 messenger there to search for it ; but after considerable expense had been in- 

 curred he returned without it. After the death of Otho, when the MSS. of 

 Rheticus, which had been in his possession, passed into the hands of James 

 Christmann, the latter discovered the canon among them, when it had been 

 given up for lost. As soon as Pitiscus knew this he examined the MSS. page 

 by page, although they were in a very bad condition (situ et squalore obsitas 

 ac pa3ne foBtentes), and to his great satisfaction found :^(1) the ten-second 

 canon of sines to 15 places, with first, second, and third differences (printed 

 in the work under notice) ; (2) sines for every second of the first and last 

 degrees of the quadrant, also to 15 places, with first and second difi'erenccs ; 

 (3) the commencement of a canon of tangents and secants, to the same 

 number of decimal places, for every ten seconds, with first and second dif- 

 ferences ; (4) a complete minute-canon of sines, tangents, and secants, also 

 to 15 decimal places. From this account, talcen in connexion with the 

 ' Opus Palatinum ' and the contents of the present work, one is able to 

 form some idea of the enormous computations undertaken by Rheticus ; 



